The correct question is not where, it is whether. And the correct answer is no. The prime minister has just announced that her cabinet will recommend where a new runway should be built. Then there will be a consultation on the decision. There is only one answer that doesn’t involve abandoning our climate change commitments and our moral scruples: nowhere.

The inexorable logic that should rule out new sources of oil, gas and coal also applies to the expansion of airports. In a world seeking to prevent climate breakdown, there is no remaining scope for extending infrastructure that depends on fossil fuels. The prime minister cannot uphold the Paris agreement on climate change, which comes into force next month, and permit the runway to be built.

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While most sectors can replace fossil fuels with other sources, this is not the case for aviation. The airline companies seek to divert us with a series of mumbo-jumbo jets, mythical technologies never destined for life beyond the press release. Solar passenger planes, blended wing bodies, hydrogen jets, algal oils, other biofuels: all are either technically impossible, commercially infeasible, worse than fossil fuels or capable of making scarcely a dent in emissions.

Aviation means kerosene. Using kerosene to hoist human bodies into the air means massive impacts. Improvements in the fuel economy of aircraft have declined to 1% a year or less, greatly outstripped by the growth in aviation. So other means must be found of trying to make it fit.

The government’s decision will be based on the findings of the Airports Commission, which reported last year. It favours a new runway at Heathrow, and proposes two means of ensuring that the extra flights will not conflict with Britain’s climate pledges. Neither is either fair or workable. The first is that the rest of the economy should make extra cuts in greenhouse gases to accommodate aviation. Already the Climate Change Act imposes a legal target of 80% reductions by 2050. But if flights are to keep growing as the commission expects, those cuts would have to rise to 85%. This is fundamentally unjust. Three-quarters of international passengers at the UK’s biggest airports travel for leisure, and they are disproportionately rich: at Heathrow their mean income is £57,000. Just 15% of people in the UK take 70% of international flights. So everyone must pay for the holidays taken by the better off.

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The alternative strategy is a carbon tax. The commission is remarkably evasive about what this entails, and its reckonings are opaque, contradictory and buried in remote annexes. Perhaps that’s unsurprising. An analysis by the Campaign for Better Transport suggests that the tax required to reconcile a new runway with our carbon commitments is somewhere between £270 and £850 for a return flight for a family of four to New York.

In other words, the Airports Commission plan amounts to increasing airport capacity then pricing people out. Where’s the sense in that?

As the commission doubtless knows, no government would impose such charges, or shut down northern airports to allow Heathrow to grow. Having approved the extra capacity, the government will discover that it’s incompatible with our commitments under the Climate Change Act, mull the consequences for a minute or two, then quietly abandon the commitments. It’s this simple: a third runway at Heathrow means that the UK will not meet its carbon targets. Hold me to that in 2050.

‘For years there has been a lively debate about the noise, local pollution and disruption caused by building a new runway at Heathrow.’ Photograph: Daniel Leal-Olivas/AFP/Getty Images

But that’s not the half of it. The Airports Commission based its projections on the work of another government body: the Committee on Climate Change. Last week the committee announced that to meet our commitments under the Paris agreement the UK will need to go much further than the 80% cut envisaged by the Climate Change Act. The Paris deal implies reductions of “at least 90%” by 2050. This is tough under any scenario, simply impossible if airport capacity grows.

It knocks the Airports Commission’s calculations out of court. If the government uses the commission’s figures to justify its decision, it will be relying on estimates that are out of date, invalid and incompatible with its international commitments.

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Don’t expect help from the opposition. On Sunday Labour’s shadow transport secretary, Andy McDonald, argued that we should pay the environmental consequences of building a new runway “full and proper heed”, then go ahead. The people of future drought zones will feel so much better when they hear about that full and proper heed.

As for the international framework, forget it. Two weeks ago 191 nations struck the world’s only agreement to regulate aviation emissions. It’s voluntary, it’s pathetic, and it relies on planting trees to offset aircraft emissions, which means replacing a highly stable form of carbon storage (leaving oil in the ground) with a highly unstable one vulnerable to loggers, fires and droughts. The meeting at which the deal was done probably caused more emissions than it will save.

For years there has been a lively debate about the noise, local pollution and disruption caused by building a new runway at Heathrow, all of which are valid concerns. But almost everyone ignores the issue that dwarfs all others. Climate change means no new runway.

If our airports are full, there’s an immediate solution. Fly less. The Free Ride campaign has proposed a just means of achieving this: curb demand by taxing frequent flyers but not those who seldom fly. (In case you’re wondering, I limit my flying to once every three years).

Is this beyond contemplation? Are we incapable of making such changes for the sake of others? If so, our ethics are weaker than those of 1791, when 300,000 British people, to dissociate themselves from slavery, stopped using sugar, reducing sales by one-third. They understood the moral implications of an act that carried no ill intent, that seemed sweetly innocent.

The perceptual gulf between us and the distant and future victims of climate change is no wider than the ocean that lay between the people of Britain and the Caribbean. If we do not make the leap of imagination that connects our actions with their consequences, it is not because we can’t, but because we won’t.

But reason has taken flight. The moral compass spins, greed and desire soar towards the stratosphere, and our conscience vanishes in the clouds. Will anyone confront this injustice?